Generalized tournament matrices with the same principal minors

A generalized tournament matrix \(M\) is a nonnegative matrix that satisfies \(M+M^{t}=J-I\), where \(J\) is the all ones matrix and \(I\) is the identity matrix. In this paper, a characterization of generalized tournament matrices with the same principal minors of orders \(2\), \(3\), and \(4\) is given. In particular, it is proven that the principal minors of orders \(2\), \(3\), and \(4\) determine the rest of the principal minors.